Triangular Prism Volume: worked example
| Triangle base | 6 |
|---|---|
| Triangle height | 4 |
| Prism length | 10 |
| Volume | 120 |
| Triangle base area | 12 |
Triangular Prism Volume: formula
Enter the base and the height of the triangular cross-section and the length of the prism, the distance between the two triangular ends. The triangle's height is perpendicular to its base. Volume is the triangle's area times the length.
Use the same unit for all three. If the triangle is defined by three sides, find its area first with Heron's formula on the triangle area calculator.
Triangular Prism Volume: changing Triangle base
| Triangle base | Volume | Triangle base area |
|---|---|---|
| 4.8 | 96 | 9.6 |
| 5.4 | 108 | 10.8 |
| 6 (example) | 120 | 12 |
| 6.6 | 132 | 13.2 |
| 7.2 | 144 | 14.4 |
Triangular Prism Volume: compare input ranges
| Input | Tested from | To | Volume: low input | Volume: high input | Swing |
|---|---|---|---|---|---|
| Triangle base | 5.4 | 6.6 | 108 | 132 | 24 (20%) |
| Triangle height | 3.6 | 4.4 | 108 | 132 | 24 (20%) |
| Prism length | 9 | 11 | 108 | 132 | 24 (20%) |
Triangular Prism Volume: individual input comparisons
| Input | Value | Volume | Triangle base area |
|---|---|---|---|
| Triangle base | 4.8 | 96 | 9.6 |
| 5.4 | 108 | 10.8 | |
| 6 | 120 | 12 | |
| 6.6 | 132 | 13.2 | |
| 7.2 | 144 | 14.4 | |
| Triangle height | 3.2 | 96 | 9.6 |
| 3.6 | 108 | 10.8 | |
| 4 | 120 | 12 | |
| 4.4 | 132 | 13.2 | |
| 4.8 | 144 | 14.4 | |
| Prism length | 8 | 96 | 12 |
| 9 | 108 | 12 | |
| 10 | 120 | 12 | |
| 11 | 132 | 12 | |
| 12 | 144 | 12 |
Triangular Prism Volume: combined input changes
| Triangle base / Triangle height | 3.2 | 4 | 4.8 |
|---|---|---|---|
| 4.8 | 76.8 | 96 | 115.2 |
| 5.4 | 86.4 | 108 | 129.6 |
| 6 | 96 | 120 | 144 |
| 6.6 | 105.6 | 132 | 158.4 |
| 7.2 | 115.2 | 144 | 172.8 |
Triangular Prism Volume: which assumptions move the result?
Triangular Prism Volume: values and definitions
| Quantity and definition | Value used |
|---|---|
| Triangle base | 6 |
| Triangle height | 4 |
| Prism length | 10 |
| Volume | 120 |
| Triangle base area | 12 |
Triangular Prism Volume: half and double Triangle base
| Triangle base | Volume |
|---|---|
| 3 | 60 |
| 6 | 120 |
| 12 | 240 |
Common error: Forgetting the one half in the triangle's area. Without it you get the volume of a box, twice the size of the wedge.
The formula assumes the ends are congruent and parallel and the sides are perpendicular to them, a right prism. An oblique prism uses the perpendicular height. Surface area needs the triangle's side lengths, which this tool does not compute.
Mixed units cause errors.
Geometry calculators: Law of Sines Calculator, Cube Calculator, Equilateral Triangle Calculator, Trigonometry Calculator, Golden Ratio Calculator, Midpoint Calculator.
A prism's volume is the area of its end shape times its length, and here that end shape is a triangle. A triangle 6 wide and 4 high covers 12, so a prism 10 long holds 120 cubic units. Roof spaces, tents and wedge-shaped planters all work this way, and the only fiddly part is measuring the triangle's height at a right angle to its base.
Take the triangle's height straight up from the base to the peak. A sloped side is longer and gives a bigger area than the triangle really has.
See the triangle area, right triangle and Pythagorean theorem calculators for the cross-section, the rectangular prism and pyramid pages for related solids, and the concrete and soil calculators in the trades categories that use volumes. The unit conversion pages convert cubic units.
Where do triangular prisms appear?
In tents, A-frame roofs, wedges, ramps and some packaging, wherever a triangular cross-section is extended along a length.
What is the volume of a triangular prism?
The area of the triangular end times the length of the prism. A triangle with area 12 and length 10 gives 120.
How do I find the triangle's area?
Half the base times the height, or use Heron's formula if you know only the three sides.